Synthetic Aperture Radar (SAR) is a powerful tool for imaging of the ground surface . Nowadays , SAR has been widely deployed as Spaceborne and airborne radar . Although , SAR was firstly designed for ground imaging , it is used as a multi-function system today . In addition of producing high resolution images , SAR can categorize targets by employing different polarization electromagnetic waves , and also can explore the height of the terrain due to its coherent property . Besides , Ground Moving Target Indication (GMTI) by SAR is an interesting topic . Since moving target causes unfocused and displaced image in the ordinary image formation algorithms , detection of moving target and estimation of its parameters can lead to have more focused and better images . Before detection and estimation , clutter should be suppressed . Some methods have been suggested for clutter rejection . As the frequency spectrum of the SAR signal varies with time , Time-Frequency analysis has been widely used in this area . In this thesis , a new method is proposed for clutter rejection and moving target detection based on detection theory and using Fractional Fourier Transform . As respects to Fractional Fourier Transforms properties , the proposed method is able to well reject the clutter , and also it has very good performance for moving target detection and doppler parameter estimation . Key Words: Clutter rejection,Ground Moving Target Indication , Ground Moving Target Imaging , Synthetic Aperture Radar